Is an artificial intelligence software or hardware?
AI or Artificial Intelligence is nothing but intelligence but in its artificial form. Intelligence comes from formation of rules and patterns in the data which is seen or on which it is trained.


For us, we programme or formulate these rules in Mathematics on which an Intelligence is created.
Ex. A neural network shows a lower level of Intelligence. It is created using basic rules of mathematics like gradient descent, derivatives and other arithmetic stuff.
These rules need a base to form themselves. Here's where computers come in. They run these rules on which intelligence thrives in binary ( or quantum sometimes ). 
But, every bit of information acquires physical space for processing and storage. Here's where hardware comes. Hardware provides the container in which  information will be processed.


Hence, for an complete AI system, computer programmes provide a soul whereas hardware provides a body/physical form for the soul.

Since, only AI is concerned, it may run on any hardware as it is a software or program or a set of mathematical rules in binary state.
Hence AI is a program.